Research Paper On Uranus
3.3. Moons of Uranus 3.3.1 Introduction
Uranus, the seventh planet of the Solar System, has 27 known moons. Uranus's moons are divided into three groups: thirteen inner moons, five major moons, and nine irregular moons. The inner moons are small dark bodies that share common properties and origins with the Uranus's rings, the five major moons (Miranda, Ariel, Umbriel, Titania, and Oberon) are massive enough to have achieved hydrostatic equilibrium. They range in diameter from 472 km for Miranda to 1578 km for Titania. While, Uranus's irregular moons range in size from 120–200 km (Sycorax) to about 20 km (Trinculo). It is worth note that “Margaret” is the only known irregular prograde moon of Uranus, and it currently has the most eccentric …show more content…
The main perturbing forces which coming from the solar influence are taken into account. The disturbing function is developed in powers of the ratio of the semimajor axes of the satellite and the Sun (6 10-3) and put in a closed form with respect to the eccentricity. The theory includes secular perturbations up to the fourth order, short, intermediate and long period perturbations up to the third order. The osculating orbital elements which describe the orbital motion of Nereid are evaluated analytically. The comparison with the numerical integration of the equations of motion gives an accuracy on the level of 0.2 km in the semimajor axis, 10-7 in the eccentricity and 10-4 degree in the angular variables over a period of several hundred …show more content…
To reach our goal we applied a successive of canonical transformations on the Hamiltonian equations. At the first stage we eliminate the short-periodic terms and take into account the eccentric anomaly of Nereid u as an independent variable, since the high eccentric orbit of Nereid precludes replacing functions of the true anomaly by expansions involving the mean anomaly. The analytical expressions of the new Hamiltonian and the determining functions are given in Saad & Kinoshita 2000). In the present study, the short-period is days, which describes the orbital revolution of Nereid around
Uranus, the seventh planet of the Solar System, has 27 known moons. Uranus's moons are divided into three groups: thirteen inner moons, five major moons, and nine irregular moons. The inner moons are small dark bodies that share common properties and origins with the Uranus's rings, the five major moons (Miranda, Ariel, Umbriel, Titania, and Oberon) are massive enough to have achieved hydrostatic equilibrium. They range in diameter from 472 km for Miranda to 1578 km for Titania. While, Uranus's irregular moons range in size from 120–200 km (Sycorax) to about 20 km (Trinculo). It is worth note that “Margaret” is the only known irregular prograde moon of Uranus, and it currently has the most eccentric …show more content…
The main perturbing forces which coming from the solar influence are taken into account. The disturbing function is developed in powers of the ratio of the semimajor axes of the satellite and the Sun (6 10-3) and put in a closed form with respect to the eccentricity. The theory includes secular perturbations up to the fourth order, short, intermediate and long period perturbations up to the third order. The osculating orbital elements which describe the orbital motion of Nereid are evaluated analytically. The comparison with the numerical integration of the equations of motion gives an accuracy on the level of 0.2 km in the semimajor axis, 10-7 in the eccentricity and 10-4 degree in the angular variables over a period of several hundred …show more content…
To reach our goal we applied a successive of canonical transformations on the Hamiltonian equations. At the first stage we eliminate the short-periodic terms and take into account the eccentric anomaly of Nereid u as an independent variable, since the high eccentric orbit of Nereid precludes replacing functions of the true anomaly by expansions involving the mean anomaly. The analytical expressions of the new Hamiltonian and the determining functions are given in Saad & Kinoshita 2000). In the present study, the short-period is days, which describes the orbital revolution of Nereid around